Regret bounds for sleeping experts and bandits

Machine Learning

Volumn 80, Issue 2-3, 2010, Pages 245-272

  Kleinberg, Robert ^a   Niculescu Mizil, Alexandru ^a,b   Sharma, Yogeshwer ^a  

^a Department of Computer Science and School of Operations Research and Information Engineering   (United States)

^b IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

Computational learning theory; Online algorithms; Regret

Indexed keywords

COMPUTATIONAL LEARNING THEORY; DECISION ALGORITHMS; MULTI ARMED BANDIT; ON-LINE ALGORITHMS; ONLINE DECISIONS; OPTIMAL REGRET; PRACTICAL PROBLEMS; REGRET;

COMPUTATION THEORY; STOCHASTIC MODELS;

LEARNING ALGORITHMS;

EID: 77955660815     PISSN: 08856125     EISSN: 15730565     Source Type: Journal    
DOI: 10.1007/s10994-010-5178-7     Document Type: Article

References (23)

1. Audibert, J.-Y., & Bubeck, S. (2009). Minimax policies for adversarial and stochastic bandits. In Proceedings of the 22nd conference on learning theory (COLT).
2. P. Auer N. Cesa-Bianchi P. Fischer 2002 Finite-time analysis of the multiarmed bandit problem Machine Learning 47 235 256 1012.68093 10.1023/A:1013689704352 (Pubitemid 34126111)
3. P. Auer N. Cesa-Bianchi Y. Freund R. E. Schapire 2002 The nonstochastic multiarmed bandit problem SIAM Journal on Computing 32 48 77 1029.68087 10.1137/S0097539701398375 1954855
4. K. Azuma 1967 Weighted sums of certain dependent random variables Tohoku Mathematical Journal 19 357 367 0178.21103 10.2748/tmj/1178243286 221571
5. Blum, A., & Mansour, Y. (2005). From external to internal regret. In Proceedings of the 18th conference on learning theory (COLT) (pp. 621-636).
6. N. Cesa-Bianchi Y. Freund D. Haussler D. P. Helmbold R. E. Schapire M. K. Warmuth 1997 How to use expert advice Journal of ACM 44 427 485 0890.68066 10.1145/258128.258179 1470152
7. Cover, T. M., & Thomas, J. A. (1999). Elements of information theory. New York: Wiley.
8. Y. Freund R. E. Schapire 1999 Adaptive game playing using multiplicative weights Games and Economic Behavior 29 79 103 0964.91007 10.1006/game.1999.0738 1729311
9. Freund, Y., Schapire, R. E., Singer, Y., & Warmuth, M. K. (1997). Using and combining predictors that specialize. In Proceedings of the 29th ACM symp. on theory of computing (STOC) (pp. 334-343).
10. Garey, M. R., & Johnson, D. S. (1979). Computers and intractability: a guide to the theory of NP-completeness. New York: Freeman.
11. J. C. Gittins 1979 Bandit processes and dynamic allocation indices Journal of the Royal Statistical Society, Series B 41 148 177 0411.62055 547241
12. J. C. Gittins D. M. Jones 1979 A dynamic allocation index for the discounted multiarmed bandit problem Biometrika 66 561 565 10.1093/biomet/66.3. 561
13. Hannan, J. (1957). Approximation to Bayes risk in repeated plays. In M. Dresher, A. Tucker, & P. Wolfe (Eds.), Contributions to the theory of games (pp. 97-139). Princeton: Princeton University Press.
14. W. Hoeffding 1963 Probability inequalities for sums of bounded random variables Journal of the American Statistical Association 58 13 30 0127.10602 10.2307/2282952 144363
15. A. T. Kalai S. Vempala 2005 Efficient algorithms for on-line optimization Journal of Computer and System Sciences 71 291 307 1094.68112 10.1016/j.jcss.2004.10.016 2168355 (Pubitemid 41278182)
16. Karp, R. M., & Kleinberg, R. (2007). Noisy binary search and its applications. In Proceedings of the 18th ACM-SIAM symp. discrete algorithms (SODA) (pp. 881-890).
17. A. Khintchine 1923 Über dyadische Brüche Mathematische Zeitschsift 18 109 116 10.1007/BF01192399 1544623
18. T. L. Lai H. Robbins 1985 Asymptotically efficient adaptive allocations rules Advances in Applied Mathematics 6 4 22 0568.62074 10.1016/0196-8858(85) 90002-8 776826
19. Langford, J., & Zhang, T. (2007). The Epoch-Greedy algorithm for multiarmed bandits with side information. In Proceedings of the 21st conference on neural information processing systems (NIPS).
20. N. Littlestone M. K. Warmuth 1994 The weighted majority algorithm Information and Computation 108 212 261 0804.68121 10.1006/inco.1994.1009 1265851 An extended abstract appeared in IEEE symposium on foundations of computer science, 1989 (pp. 256-261)
21. H. Robbins 1952 Some aspects of the sequential design of experiments Bulletin of the American Mathematical Society 58 527 535 0049.37009 10.1090/S0002-9904-1952-09620-8 50246
22. Vovk, V. G. (1990). Aggregating strategies. In Proceedings of the 3rd conference on learning theory (COLT) (pp. 371-386).
23. V. G. Vovk 1998 A game of prediction with expert advice Journal of Computer and System Sciences 56 153 173 0945.68528 10.1006/jcss.1997.1556 1629690 An extended abstract appeared in COLT, 1995 (pp. 51-60)